proposed

approved

editing

proposed

Sum2c[a_, b_] := Sum2c[a, b] = If[0 == a || 0 == b, Return[0], ], Return[ Sum2c[BitXor[a, b], 2*BitAnd[a, b]] + 1]];

Return[Sum2c[BitXor[a, b], 2*BitAnd[a, b]] + 1]];

a[n_] := Sum2c[n - (1/2)*trinv[n]*(trinv[n] - 1), (trinv[n] - 1)*(trinv[ n]/2 + 1), ) - n];

(trinv[n] - 1)*(trinv[n]/2 + 1) - n];

Table[a[n], {n, 0, 120}]}](* _Jean-François Alcover_, Mar 07 2016, adapted from Maple *)

trinv[n_] := Floor[(1/2)*(Sqrt[8*n + 1] + 1)];

Sum2c[a_, b_] := Sum2c[a, b] = If[0 == a || 0 == b, Return[0],

Return[Sum2c[BitXor[a, b], 2*BitAnd[a, b]] + 1]];

a[n_] := Sum2c[n - (1/2)*trinv[n]*(trinv[n] - 1),

(trinv[n] - 1)*(trinv[n]/2 + 1) - n];

Table[a[n], {n, 0, 120}]

approved

editing

_Antti Karttunen _, Jun 22 1999

OEIS Server: https://oeis.org/edit/global/2208

nonn,tabl,new

Antti.Karttunen@iki.fi (karttu@megabaud.fi) 22-JUN-1999

Antti Karttunen Jun 22 1999

Recursion counts for summation table A003056 with formula a(0,x) = x, a(y,0) = y, a(y,x) = a((y XOR x),2*(y AND x))

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 3, 2, 3, 1, 3, 2, 3, 0, 0, 1, 3, 3, 2, 2, 3, 3, 1, 0, 0, 2, 1, 3, 2, 1, 2, 3, 1, 2, 0, 0, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 0, 0, 3, 2, 3, 1, 3, 1, 3, 1, 3, 2, 3, 0, 0, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 0

0,12

a(n) -> add2c( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) )

add2c := proc(a, b) option remember; if((0 = a) or (0 = b)) then RETURN(0); else RETURN(1+add_c(XORnos(a, b), 2*ANDnos(a, b))); fi; end;

Cf. A050600, A050602, A003056, A048720 (for the Maple implementation of trinv and XORnos, ANDnos)

nonn,tabl

Antti.Karttunen@iki.fi (karttu@megabaud.fi) 22-JUN-1999

approved